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\begin{equation}
\begin{aligned}
&amp; \uuline{e^{\frac{1}{2} x} y^{\prime}+\frac{1}{2} e^{\frac{1}{2} x} y}=\frac{3}{2} e^{\frac{1}{2} x} \rightarrow \frac{\textrm{d}}{\textrm{d} x}\left(e^{\frac{1}{2} x} y \right)=\frac{3}{2} e^{\frac{1}{2} x}\\
&amp; \rightarrow e^{\frac{1}{2} x} y =3 e^{\frac{1}{2} x} +C \rightarrow y=3+Ce^{-\frac{1}{2}x},
\end{aligned}\tag{2.1.5}
\end{equation}
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